Dr. Bailyn received his B.Sc. in Astronomy and Physics from Yale (1981) and completed his Ph.D. in Astronomy at Harvard (1987). His research interests are concentrated in High Energy Astrophysics and Galactic Astronomy, with a focus on observations of binary star systems containing black holes. His latest book, What Does a Black Hole Look Like?addresses lingering questions about the nature of Dark Matter and black holes, and is accessible to a variety of audiences.

Now, on to the questions!

PUP: What inspired you to get into your field?

Charles D. Bailyn: Like a lot of little kids in the late 1960s, I was fascinated by space travel, and I wanted to be an astronaut. But then someone told me about space sickness – I’m prone to motion sickness, and that sounded pretty awful to me. So “astronaut” morphed into “astrophysicist” – I liked the idea of exploring the universe through math and physics. In college I thought I would work on relativity theory, but I didn’t quite have the mathematical prowess for that, and around that time I found out that the X-ray astronomers were actually observing black holes and related objects. So as a graduate student and post-doc I gradually moved from being a theorist to being an observer. I’ve analyzed data from many of NASA’s orbiting observatories, so I ended up being involved with the space program after all.

What would you have been if not an astronomer?

I’ve always loved music, particularly vocal music, and I’ve spent a lot of time in and around various kinds of amateur singing groups. I could easily see myself as a choral conductor.

What is the biggest misunderstanding that people have about astronomy?

Well, I’m always a bit amused and dismayed when I tell someone that I’m an astronomer, and they ask “what’s your sign?” – as if astronomy and astrology are the same thing. I used to tell people very seriously that I’m an Orion – this is puzzling, since most people know it’s a constellation but not part of the zodiac. At one point I had an elaborate fake explanation worked out about how this could be.

Why did you write this book? Who do you see as its audience?

There seem to be two kinds of books on black holes and relativity – books addressing a popular audience that use no math at all, and textbooks that focus on developing the relevant physical theory. This book was designed to sit in the middle. It assumes a basic knowledge of college physics, but instead of deriving the theory, its primary concerns are the observations and their interpretation. I’m basically talking to myself as a sophomore or junior in college.

“The unseen parts of the Universe are the most intriguing, at least to me.”

How did you come up with the title?

The Frontiers in Physics (Princeton) series like to have questions in the title, and this one is particularly provocative. Black holes by definition cannot be seen directly, so asking what they “look like” is a bit of an oxymoron. But a lot of modern astrophysics is like that – we have powerful empirical evidence for all sorts of things we can’t see, from planets around distant stars to the Dark Matter and Dark Energy that make up most of the stuff in the Universe. The unseen parts of the Universe are the most intriguing, at least to me.

What are you working on now?

I’m turning the online version of my introductory astronomy course into a book – kind of a retro move, turning online content into book format! It will be for a non-scientific rather than a scientific audience. But mostly I’m doing administrative work these days – I’m currently in Singapore serving as the inaugural Dean of Faculty for Yale-NUS College, the region’s first fully residential liberal arts college. The importance of science in a liberal arts curriculum is a passion of mine – after all, astronomy was one of the original liberal arts – and I’m glad to have a chance to bring this kind of education to a new audience, even though it takes me away from my scientific work for a while.

What are you reading right now?

I’ve been following the reading list for our second semester literature core class, starting from Don Quixote and Journey to the West, the first early modern novels in the European and Chinese traditions respectively, ending with Salman Rushdie, who is all about the interaction of East and West. It’s fun being a student again!

As many of you will know, in November 2013, the remarkable astrophysicist, Dimitri Mihalas – a pioneering mind in computational astrophysics, and a world leader in the fields of radiation transport, radiation hydrodynamics, and astrophysical quantitative spectroscopy – passed away. Though deeply saddened by this news, I also feel a unique sense of honor that, this year, I am able to announce the much-anticipated text, Theory of Stellar Atmospheres: An Introduction to Astrophysical Non-equilibrium Quantitative Spectroscopic Analysis, co-authored by Ivan Hubeny and Dimitri Mihalas. This book is the most recent publication in our Princeton Series in Astrophysics (David Spergel, advising editor), and it is a complete revision of Mihalas’sStellar Atmospheres, first published in 1970 and considered by many to be the “bible” of the field. This new edition serves to provide a state of the art synthesis of the theory and methods of the quantitative spectroscopic analysis of the observable outer layers of stars. Designed to be self-contained, beginning upper-level undergraduate and graduate-level students will find it accessible, while advanced students, researchers, and professionals will also gain deeper insight from its pages. I look forward to bringing this very special book to the attention of a wide readership of students and researchers.

It is also with profound excitement that I would like to announce the imminent publication of Kip Thorne and Roger Blandford’sModern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. This is a first-year, graduate-level introduction to the fundamental concepts and 21st-century applications of six major branches of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn’t. Early readers have described the manuscript as “splendid,” “audacious,” and a “tour de force,” and I couldn’t agree more. Stay tuned!

Lastly, it is a pleasure to announce a number of newly and vibrantly redesigned books in our popular-level series, the Princeton Science Library. These include Richard Alley’sThe Two-Mile Time Machine, which Elizabeth Kolbert has called a “fascinating” work that “will make you look at the world in a new way” (The Week), as well as G. Polya’s bestselling must-read, How to Solve It. In addition, the classics by Einstein, The Meaning of Relativity, with an introduction by Brian Greene, and Feynman, QED, introduced by A. Zee, are certainly not to be missed.

Of course, these are just a few of the many new books on the Princeton list I hope you’ll explore. My thanks to you all—readers, authors, and trusted advisors—for your enduring support. I hope that you enjoy our books and that you will continue to let me know what you would like to read in the future.

All this week for World Space Week, we’ve been posting excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration, and while that’s an amazing book, we decided that in order to give World Space Week all of the cosmic attention it deserves, we would put together an interstellar round-up to fire up your engines and blast you to infinity… and beyond!

This book describes the startling discoveries being made in the very real science of astrobiology, an intriguing new field that blends astronomy, biology, and geology to explore the possibility of life on other planets. This book goes beyond UFOs to discuss some of the tantalizing questions astrobiologists grapple with every day: What is life and how does it begin? What makes a planet or moon habitable? Is there life on Mars or elsewhere in the solar system? How can life be recognized on distant worlds? Is it likely to be microbial, more biologically complex–or even intelligent? What would such a discovery mean for life here on Earth?

In the early 1980s, when the two Voyager spacecraft skimmed past Titan, Saturn’s largest moon, they transmitted back enticing images of a mysterious world concealed in a seemingly impenetrable orange haze. Titan Unveiled is one of the first general interest books to reveal the startling new discoveries that have been made since the arrival of the Cassini-Huygens mission to Saturn and Titan.

The birth and evolution of our solar system is a tantalizing mystery that may one day provide answers to the question of human origins. This book tells the remarkable story of how the celestial objects that make up the solar system arose from common beginnings billions of years ago, and how scientists and philosophers have sought to unravel this mystery down through the centuries, piecing together the clues that enabled them to deduce the solar system’s layout, its age, and the most likely way it formed.

Belbruno devised one of the most exciting concepts now being used in space flight, that of swinging through the cosmos on the subtle fluctuations of the planets’ gravitational pulls. His idea was met with skepticism until 1991, when he used it to get a stray Japanese satellite back on course to the Moon. The successful rescue represented the first application of chaos to space travel and ushered in an emerging new field. Part memoir, part scientific adventure story, Fly Me to the Moon gives a gripping insider’s account of that mission and of Belbruno’s personal struggles with the science establishment.

This book offers an intimate guide to the Milky Way, taking readers on a grand tour of our home Galaxy’s structure, genesis, and evolution, based on the latest astronomical findings. In engaging language, it tells how the Milky Way congealed from blobs of gas and dark matter into a spinning starry abode brimming with diverse planetary systems–some of which may be hosting myriad life forms and perhaps even other technologically communicative species. It vividly describes the Milky Way as it appears in the night sky, acquainting readers with its key components and telling the history of our changing galactic perceptions.

The Hubble Space Telescope has produced the most stunning images of the cosmos humanity has ever seen. It has transformed our understanding of the universe around us, revealing new information about its age and evolution, the life cycle of stars, and the very existence of black holes, among other startling discoveries. But it took an amazing amount of work and perseverance to get the first space telescope up and running. The Universe in a Mirror tells the story of this telescope and the visionaries responsible for its extraordinary accomplishments.

Think you know all about missions in space? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

Houston, we have lift off!

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter(s) about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today we have two excerpts. The first is from Chapter 10, and it describes some of the leaps and bounds we have been able to make in black hole exploration thanks to Chandra. The second excerpt is from Chapter 11, which talks about what is probably the most famous spacecraft, the Hubble Space Telescope.

Tomorrow will bring another chapter and another adventure, so stay tuned!

Chandra has the sensitivity to detect stellar black holes hundreds of light-years away. Only about twenty binary systems have well-enough measured masses to be sure the dark companion is a black hole, but X-ray observations can be used to identify black holes with fairly high reliability. The examples studied with X-ray telescopes are the brightest representatives of a population of about 100 million black holes in the Milky Way.
X-ray observations have also pushed the limit of our understanding of black holes. In 2007, a research team used Chandra to discover a black hole in M33, a nearby spiral galaxy. The black hole was sixteen times the mass of the Sun, making it the most massive stellar black hole known.32 Moreover, it was in a binary orbit with a huge star seventy times the Sun’s mass. The formation mechanism of the black hole that placed it in such a tight embrace with its companion is unknown. This is the first black hole in a binary system that shows eclipses, which provides unusually accurate measurements of mass and other properties. The massive companion will also die as a black hole, so future astronomers will be able to gaze on a binary black hole where energy is lost as gravitational radiation and the two black holes dance a death spiral as they coalesce into a single beast.

Above all scientific projects, the Hubble Space Telescope encapsulates and recapitulates the human yearning to explore distant worlds, and understand our origins and place in the universe. Its light grasp is 10 billion times better than Galileo’s best spyglass, and many innovations were needed for it to be realized: complex yet reliable instruments, the ability for astronauts to service the telescope, and the infrastructure to support the projects of thousands of scientists from around the world. The facility and its supporters experienced failure and heartache as well as eventual success and vindication.
Hubble’s legacy has touched every area of astronomy, from the Solar System to the most distant galaxies. In the public eye, it’s so well known that many people think it’s the only world-class astronomy facility. In fact, it operates in a highly competitive landscape with other space facilities and much larger telescopes on the ground. Although it doesn’t own any field of astronomy, it has made major contributions to all of them. It has contributed to Solar System astronomy and the characterization of exoplanets, it has viewed star birth and death in unprecedented detail, it has paid homage to its namesake with spectacular images of galaxies near and far, and it has cemented important quantities in cosmology, including the size, age, and expansion rate of the universe.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

Houston, we have lift off!

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter(s) about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today we have two excerpts. The first is from Chapter 8, which talks about the first star charts, which were created by the Greek astronomer, Hipparchus (for whom the Hipparcos was named). The second excerpt is from Chapter 9, explaining some of the adversities Spitzer had to face before it was able to go into space.

Tomorrow will bring another chapter and another adventure, so stay tuned!

For thousands of years, all we’ve known of Hipparchus’s star guide were descriptions by Ptolemy. But astronomer Bradley Schaefer asserts that, indeed, the Farnese Atlas, a statue of the Greek figure Atlas kneeling while holding on his shoulders a globe of constellations, represents the stars and constellations known to the ancient Greeks. He contends that the statue “is the oldest surviving depiction of the set of the original Western constellations, and as such can be a valuable resource for studying their early development.”18 Schaefer realized after a detailed study of the globe that the constellations depicted match the night sky in the era and from the location where Hipparchus lived in 129 BC. As evidence in favor of this possibility, Schaefer writes: “First, the constellation symbols and relations are identical with those of Hipparchus and are greatly different from all other known ancient sources. Second, the date of the original observations is 125 ± 55 BC, a range that includes the date of Hipparchus’s star catalogue (c. 129 BC) but excludes the dates of other known plausible sources.” Schaefer concludes that “the ultimate source of the position information [of the constellations on the globe] used by the original Greek sculptor was Hipparchus’s data.”

Spitzer, from its earliest inception, was especially designed for infrared astronomy and is sensitive enough to detect infrared signatures of stars and galaxies billions of light-years away. The space telescope has been instrumental in unveiling small, dim objects like dwarf stars and exoplanets and can even determine the temperature of their slender atmospheres. Originally proposed in the late 1970s as NASA’s Space Infrared Telescope Facility, the Spitzer Space Telescope suffered from uncertainty, a delay after the loss of the space shuttle Challenger, near-cancellation, congressional limbo, budget cuts, and “descoping.” Nevertheless, in 2003 the telescope was finally launched, after being renamed subsequent to a public opinion poll conducted by NASA. The last of NASA’s four Great Observatories, the $800 million telescope was named after Lyman Spitzer, an early advocate of the importance of orbital telescopes.13 After launch, the spacecraft took about 40 days to cool to its operating temperature of 5 Kelvin. Once cooled, it took just an ounce of liquid helium per day to maintain its detectors at their operating temperature. A solar panel facing the Sun serves to gather power and protect the telescope from radiation.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

Houston, we have lift off!

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter(s) about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today we have two excerpts. The first is from Chapter 6, and our excerpt talks about how Stardust was able to keep up with the intense speed of the Wild 2 comet to photograph it. The second excerpt is from Chapter 7, which describes “space weather”, which SOHO is able to track to warn us of any changes in our solar system.

Tomorrow will bring another chapter and another adventure, so stay tuned!

Mission controllers tried to sneak up behind Wild 2 to minimize the relative speed of the two objects. Even so Stardust was moving 13,000 mph, or five times the speed of a rifle bullet, as it flew through the glowing coma of the comet. It took seventy-two close-up photographs. That may not seem like many, but keeping the relatively small comet in the camera field of view during such a fleeting and high-speed encounter was a major feat.10 The images showed a surface riddled with depressions with flat bottoms and sheer walls, ranging in size from dozens of meters to several kilometers. The comet itself is irregular in shape and five kilometers in diameter. The features are impact craters and gas vents; ten vents were active when Stardust flew by.
The neatest trick Stardust had up its sleeve was gathering material from the comet tail. [...] All of the solid objects in the universe were built from microscopic dust particles—stardust. The probe was designed to capture material too small to see in its eight-minute ride through the comet’s tail and then its long ride home.

Data from SOHO, and increasing concern over the impact of space weather, caused NASA to commission a new study in 2009. The resulting report provides clear economic data to quantify the risk to the near-Earth environment from episodes of intense solar activity. Extreme space weather is in a category with other natural hazards that are rare but have far-reaching consequences, like major earthquakes and tsunamis.34 It’s likely that more than once in the next twenty years there will be an “electro-jet disturbance” that disrupts the national power grid. In the 1989 event, the loss of some portions of the grid put stress on others and led to a cascade affect. The end result was power outages affecting more than 130 million people and covering half the country.
SOHO cannot prevent these natural disasters, but it can give two or three days’ notice of Earth-directed disturbances. And as we become more accurate in anticipating space storms, operators can place satellites in protective modes, shut down or limit power grids, redirect commercial flights, warn oceanic cruise and cargo ships, and place astronauts working on the International Space Station in the safest possible location on the station. Such steps will not only save lives but also protect the information systems that sustain our electronically fragile and networked global community.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

Houston, we have lift off!

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter(s) about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today we have two excerpts. The first is from Chapter 4, and our excerpt does its best to describe exactly how far away the Voyager spacecrafts are, and how completely wild that is. The second excerpt is from Chapter 5, which describes the way in which Cassini travels around Saturn without getting sucked into its gravitational pull.

Tomorrow will bring another chapter and another adventure, so stay tuned!

To see why these spacecraft represented such a leap in our voyaging through space, consider a scale model of the Solar System where the Earth is the size of a golf ball. On this scale, the Moon is a grape where the two objects are held apart with outstretched arms. That gap is the farthest humans have ever traveled, and it took $150 billion at 2011 prices to get two dozen men there. Mars on this scale is the size of a large marble at the distance of
1,100 feet at its closest approach. As we’ve seen, it took an arduous effort spanning more than a decade before NASA successfully landed a probe on our nearest neighbor. A very deep breath is needed to explore the outer Solar System. In our scale model, Jupiter and Saturn are large beach balls 1.5 and 3.5 miles away from Earth, respectively, and Uranus and Neptune are soccer balls 7 and 12 miles from the Earth. This large step up in distance was a great challenge for spacecraft designers and engineers. On this scale, the Voyager 1 and 2 spacecraft are metallic “motes of dust” 48 and 37 miles from home, respectively.

Over its core mission, Cassini orbited Saturn 140 times. To see Saturn, its rings, its largest moons, and its magnetosphere from all conceivable angles, Cassini is using its rockets and seventy gravity-assist flybys of Titan to tweak its orbit size, period, velocity, and inclination from Saturn. As the largest moon, Titan isthe most useful in “steering” Cassini around the Saturnian system. Each Titan flyby is engineered to return Cassini into the proper trajectory for its next Titan flyby. Encounters with other moons are performed opportunistically with what’s called a targeted flyby. About fifteen are planned by the end of the mission, half to the intriguing small moon Enceladus. From 2004 through 2011, Cassini did a dizzying hundred flybys, with another dozen completed in 2012. NASA hosts a clock counting down the time until the next swooping visit to a moon and coyly calls these “Tour Dates” to appeal to a younger generation.26 By clever planning, NASA engineers have doubled the length of the mission even though just a quarter tank of fuel remains.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today’s excerpt is from Chapter 3, and it talks about our strategy for learning more about Mars, and what the Mars Rovers, Spirit and Opportunity, are doing to help us with that.

Tomorrow will bring another chapter and another adventure, so stay tuned!

Decoding the Red Planet

As we saw in the last chapter, Mars seems dead to the orbiters that daily send back images of the surface. The atmosphere is tenuous, ultraviolet radiation and cosmic rays scorch the soil, and it rarely gets above freezing even on the balmiest summer day.15 It’s unlikely any form of life could exist on the surface now, but Mars has not always been so inhospitable. NASA’s strategy in searching for life in the Solar System is to “follow the water,” and even if there’s no surface water now, there was in the past. Each of the Mars Exploration Rovers, Spirit and Opportunity, was designed for just a ninety-day mission. In the end, they have vastly exceeded expectations with their indomitable traverses of the forbidding Martian terrain. Think of them as twin robotic field geologists whose primary goal is to search for the signposts of water.16 The record of past water can be found in the rocks, minerals, and landforms on Mars, particularly those that could only have formed in the presence
of water.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

All week long for World Space Week, we will be posting exclusive excerpts from Chris Impey and Holly Henry’s new book, Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration. Each day will include an excerpt from a different chapter about a different unmanned spacecraft, along with a picture of the craft that doubles as an iPhone background!

Today’s excerpt is from Chapter 2, and it discusses what it was like when, in 1976, we first landed a spacecraft on Mars.

Tomorrow will bring another chapter and another adventure, so stay tuned!

The Vikings Reach Mars

On July 20, 1976, a small spacecraft emerged from a cloudless, apricot-colored Martian sky and fell toward the western Chryse Planitia, the “Golden Plain.” Its heat shield glowed as it buffeted through the tenuous atmosphere.27 About four miles up, the parachutes deployed, the heat shield was jettisoned, and three landing legs unfolded like a claw. At one mile up, the retrorockets fired, and less than a minute later the Viking 1 lander decelerated to six miles per hour, reaching the surface with a slight jolt.28 It was a landmark of technological prowess, the first time humans had ever soft-landed an emissary on another planet. The twin Viking missions were the most complex planetary probes ever designed. Their total price tag was around $1 billion, equivalent to $4 billion today after adjusting for inflation. That can be compared to the $80 million cost of Mariner 4. Mission planners were well aware of the challenges; the Soviets had previously failed four times to soft land on Mars.29 Each Viking consisted of an orbiter designed to image the planet and a lander equipped to carry out detailed experiments on the surface.30 For the most part, the hardware worked flawlessly, but there were tense moments for the engineers and scientists on the team. After ten months and 100 million miles of traveling, the Vikings reached Mars two weeks apart.

Think you know all about these missions? Take our quiz and find out!
Proud of your score? Tweet it! #WSW2013

In honor of the 2013 World Space Week, we are celebrating all week long with all sorts of space-themed articles, quizzes, pictures, and more! To start of the week, which last from October 4th-10th, we put together a little quiz about some of the most famous and important unmanned space explorations in our nation’s history.
Feeling a little stumped? Fear not! Pick up a copy of Chris Impey and Holly Henry’s brand new book, titled Dreams of Other Worlds: The Amazing Story of Unmanned Space Exploration, which talks all about spacecrafts, probes, telescopes, rovers, and of course, the solar system.

Comment what your score is below and if you want to see the answers, click here.
Proud of your score? Tweet it! #WSW2013

William H. Waller, astronomist and author of The Milky Way: An Insider’s Guide, recently wrote an article that was picked up by The Huffington Post for their blog. Based on this bio page that was also posted for Waller on HuffPost, we’re hoping this means he will be writing regularly about science and the stars, especially with some of the amazing pictures included in the article.

The post, which focuses on our ability to visibly see the Milky Way with all of the light pollution in the air, starts by saying:

“For most of human history, the night sky demanded our attention. The shape-shifting Moon, wandering planets, pointillist stars, and occasional comet enchanted our sensibilities while inspiring diverse tales of origin. The Milky Way, in particular, exerted a powerful presence on our distant ancestors. Rippling across the firmament, this irregular band of ghostly light evoked myriad myths of life and death among the stars. In 1609, Galileo Galilei pointed his telescope heavenward and discovered that the Milky Way is “nothing but a congeries of innumerable stars grouped together in clusters.” Fast forward 400 years to the present day, and we find that the Milky Way has all but disappeared from our collective consciousness. Where did it go?”

This book offers an intimate guide to the Milky Way, taking readers on a grand tour of our home Galaxy’s structure, genesis, and evolution, based on the latest astronomical findings. In engaging language, it tells how the Milky Way congealed from blobs of gas and dark matter into a spinning starry abode brimming with diverse planetary systems–some of which may be hosting myriad life forms and perhaps even other technologically communicative species.

Waller makes the case that our very existence is inextricably linked to the Galaxy that spawned us. Through this book, readers can become well-informed galactic “insiders”–ready to imagine humanity’s next steps as fully engaged citizens of the Milky Way.

William H. Waller is an astronomer, science educator, and writer. He lives with his family in Rockport, Massachusetts, where he can still see the Milky Way on dark moonless nights.

It is no coincidence that trigonometry up until the sixteenth century was developed mainly by astronomers. Aristarchus and Hipparchus, who founded trigonometry as a distinct branch of mathematics, were astronomers, as was Ptolemy, the author of the Almagest. During the Middle Ages, Arab and Hindu astronomers, notably Abul-Wefa, al-Battani, Aryabhata, and Ulugh Beg of Samarkand (1393-1449), absorbed the Greek mathematical heritage and greatly expanded it, especially in spherical trigonometry. And when this combined heritage was passed on to Europe, it was again an astronomer who was at the forefront: Johann Muller, known as Regiomontanus.

Regiomontanus was the first publisher of mathematical and astronomical books for commercial use. In 1474 he printed his Ephemerides, tables listing the position of the sun, moon, and planets for each day from 1475 to 1506. This work brought him great acclaim; Christopher Columbus had a copy of it on his fourth voyage to the New World and used it to predict the famous lunar eclipse of February 29, 1504. Regiomontanus’s most influential work was his De triangulis omnimodis (On triangles of every kind), a work in five parts (“books”) modeled after Euclid’s Elements. As he states in his introduction, Regiomontanus’s main goal in On Triangles was to provide a mathematical introduction to astronomy. Regiomontanus completed writing On Triangles in 1464, but it was not published until 1533, more than half a century after his death.

Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine, and their trigonometric relatives, he brings the subject to life in a compelling blend of history, biography, and mathematics. He presents both a survey of the main elements of trigonometry and a unique account of its vital contribution to science and social development. Woven together in a tapestry of entertaining stories, scientific curiosities, and educational insights, the book more than lives up to the title Trigonometric Delights.

Maor also sketches the lives of some of the intriguing figures who have shaped four thousand years of trigonometric history. We meet, for instance, the Renaissance scholar Regiomontanus, who is rumored to have been poisoned for insulting a colleague, and Maria Agnesi, an eighteenth-century Italian genius who gave up mathematics to work with the poor–but not before she investigated a special curve that, due to mistranslation, bears the unfortunate name “the witch of Agnesi.” The book is richly illustrated, including rare prints from the author’s own collection. Trigonometric Delights will change forever our view of a once dreaded subject.